Series Lab: Geometric Sums and Taylor Polynomials

MTH-117 · Semester I · Mathematics I

Limits of quotients

Guided practice — solve each problem, check, then generate a fresh one.

Score 0 / 0

Formula to apply

lim_{x→a} (x² − a²)/(x − a) = 2a

Problem

Evaluate lim_{x→3} (x² − 9) / (x − 3).

Working

  1. 1Factor the numerator: x² − 9 = (x − 3)(x + 3).
  2. 2Cancel: f(x) = x + 3 for x ≠ 3.
  3. 3Substitute x = 3: the limit is 3 + 3 = 6.